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Thermodynamics and Phase Transition of Spherically Symmetric Black Hole in de Sitter Space from Rényi Statistics

Schwarzschild black holes in a de Sitter background were studied in terms of their thermodynamics based on the Rényi statistics. This led to thermodynamically stable black hole configurations for some certain range of black hole radii; namely within this range the corresponding black holes have positive heat capacity. Moreover, for a certain background temperature there can exist at most three configurations of black hole; one among which is thermodynamically stable. These configurations were investigated in terms of their free energies, resulting in the moderate-sized stable black hole configuration being the most preferred configuration. Furthermore, a specific condition on the Rényi non-extensive parameter is required if a given hot spacetime were to evolve thermally into the moderate-sized stable black hole.